Question

1. Determine whether the lines are parallel, perpendicular or neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 = (z-2)/6

2. A) Find the line intersection of vector planes given by the equations -2x+3y-z+4=0 and 3x-2y+z=-2

B) Given U = <2, -3, 4> and V= <-1, 3, -2> Find a. U . V b. U x V

Answer #1

1. Solve all three:
a. Determine whether the plane 2x + y + 3z – 6 = 0 passes
through the points (3,6,-2) and (-1,5,-1)
b. Find the equation of the plane that passes through the points
(2,2,1) and (-1,1,-1) and is perpendicular to the plane 2x - 3y + z
= 3.
c. Determine whether the planes are parallel, orthogonal, or
neither. If they are neither parallel nor orthogonal, find the
angle of intersection:
3x + y - 4z...

The equations of three lines are given below Line 1: y=3x-5 Line
2: y=-1/3x +1 Line 3: 3x-9y=18 For each pair of lines, determine
whether they are parallel, perpendicular, or neither: 1. Line 1 and
2 are they (parallel, perpendicular, or neither.) 2. Line 1 and 3
are they (parallel, perpendicular, or neither.) 3. Line 2 and 3 are
they (parallel, perpendicular, or neither.

Examine whether or not these pair of lines are perpendicular to
each other. (1) y - 3x - 2 = 0 and 3y + x + 9 = 0 (2) 3y - 4 = 2x +
3 and y-5 = x+ 6 (3) Find the equations of the tangent and normal
to the curve xsquare + ysquare+3xy-11 = 0 at the point x = 1, y =
2.

Show that the two lines with equations (x, y, z) = (-1, 3,
-4) + t(1, -1, 2) and (x, y, z) = (5, -3, 2) + s(-2, 2,
2) are perpendicular. Determine how the two lines
interact.
Find the point of intersection of the line (x, y, z) = (1,
-2, 1) + t(4, -3, -2) and the plane x – 2y + 3z =
-8.

given the planes P1 and P2 determine whether the planes intersect
or are parallel. if they intersect, give the direction vector for
thr line of intersection. P1:3x+y-3z=4
p2:2x+3y+2z=6

Determine whether the lines l1: x = 2 +
u, y = 1 + u, z = 4 + 7u and
l2: x = -4 + 5w;
y = 2 - 2w, z = 1 - 4w intersect, and if so, find
the point of intersect, and the angles between
the lines.

The planes x + 3 y − 2 z = 1 and 2 x − y + 3 z = 4 intersect in
a line. A direction vector for this line is given by:

Given the following pairs of lines, determine whether they are
parallel, intersecting or skew, if they intersect, find the
intersecting and the plane containing them.
1) L1: (x-1)/1=(y-2)/1=(z-3)/-2
L2:(x-1)/1=(y-3)/0=(z-2)/-1
2) L1: x=t, y=-t,z=-1 L2: x=s, y=s,
z=5
2) L1: (3+2x)/0=(-3+2y)/1=(6-3z)/2 L2:
x=5/2, y=(3/2)-3t, z=2+4t

1) Solve these equations: 3x-y=-11
x+2y=8
2) Solve these equations:
x+y+z=6
x-y-z=-4
2x+y-4z=-8

solve the system of equations
1: y=3x^2-2x-1
2x+3y=2
2: x^2+(y-2)^2=4
x^2-2y=0

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